ok, so i still dont have the actual figure for % yield for carbon-11, but if it were 0.1%, then the amount in a reactor when you shut it down will equal the equilibrium value reached during continuous operation; as above, we have 7.18 x 10^18 reactions per second; hypothetically * 0.001 = 7.18 x 10^15 carbon-11 atoms created per second. (x 20.334 minutes = 8.76 x 10^18 atoms created during one half-life period).
at equilibrium, decay rate equals creation rate, so there would be twice this, or 1.752 x 10^19 atoms in the reactor, when you shut it down, or 320 micrograms.
make adjustments for actual yield
To put it in context another way: If you were standing 1m from a naked source of those 1.7x10^19 atoms of C-11 with no shielding for a few hours (ie long enough for pretty much all of it to decay) then the dose you’d get would definitely be lethal.
Working as follows:
Most C-11 decays via positron emission - with a range of energies averaging a few hundred keV. the positron will then annihilate producing two ~511keV gammas back to back.
If we discount the positrons themselves (since they won’t get very far) and just have the dose due to the gammas
gamma energy = 1.022MeV = 1.022e6*1.6022e-19 = 1.64e-13 J
1.752 x 10^19 atoms * 1.64e-13 J/decay =2.87e6 J total
fraction of surface area of sphere of a person at 1m ~ 8%
8%* 2.87e6 J = 2.30e5 J
energy distributed over ~75kg => 2.3e5/75 ~ 3000 J/kg
So you’d get very roughly 3000Gy dose!!!
Of course you’d actually get nothing like that much in reality since most of the decay energy would end up being absorbed close to the source and converted to heat, but still you get the idea that it’s a really good idea not to go in and service the device for at least 8 hours after turning it off.
After 8 hours (or ~24 half lives) the activity will have dropped to 0.5^24 =6e-8 times lower, so your dose working for a day after waiting the first 8 hours would be around 3000*6e-8 = 0.2mGy which is liveable, but still too high to meet the ALARP principle
If you wait an extra few hours, so 12 total (36 half lives) then the remaining potential dose drops to roughly 3000*1.4e-11 or around 40nGy - much more acceptable.
The question is: Is C-11 the longest lived of the by-products? The design of the device, down to the last nut & bolt will need to be considered when working out the actual dose limits. For example, some 1st & 2nd Gen fission reactors had a little cobalt in the structural steel alloys - this with its ~5yr half life now makes up a major part of the decommissioning burden.